Solve the system: x + y = 7 and 2x - y = 3.

Solve the system: x + y = 7 and 2x - y = 3.

• A. (3, 4)
• B. (7, 0)
• C. (10/3, 11/3)
• D. (2, 5)

Answer: (C)

Solving a system of linear equations by eliminating a variable. When two equations hold at the same time, you can add or subtract them to cancel one variable and solve for the other. For x plus y equals 7 and 2x minus y equals 3, add the two equations to cancel y: (x + y) + (2x − y) = 7 + 3, which gives 3x = 10, so x = 10/3. Then substitute this value into x + y = 7 to find y: y = 7 − 10/3 = 21/3 − 10/3 = 11/3. So the solution is (10/3, 11/3). The other pairs don’t satisfy both equations. For example, (3, 4) makes x + y = 7 but 2x − y = 2, not 3; (7, 0) makes 2x − y = 14; (2, 5) makes 2x − y = −1.

Solving a system of linear equations by eliminating a variable. When two equations hold at the same time, you can add or subtract them to cancel one variable and solve for the other.

For x plus y equals 7 and 2x minus y equals 3, add the two equations to cancel y: (x + y) + (2x − y) = 7 + 3, which gives 3x = 10, so x = 10/3. Then substitute this value into x + y = 7 to find y: y = 7 − 10/3 = 21/3 − 10/3 = 11/3. So the solution is (10/3, 11/3).

The other pairs don’t satisfy both equations. For example, (3, 4) makes x + y = 7 but 2x − y = 2, not 3; (7, 0) makes 2x − y = 14; (2, 5) makes 2x − y = −1.